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Spectral gap in simple Lie groups : Clay Mathematics Institute Senior Scholar Lecture.

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Interactions between Dynamics of Group Actions and Number Theory

Consider two matrices a , b in the orthogonal group SO(d) that span a dense subgroup. We will first recall that, in dimension at least 3, for n large, the set of words of length n in a and b become equidistributed in SO(d). We will then see that, when the matrices a, b have algebraic coefficients, the precision of this equidistribution is exponentially small in n. This joint work with N. de Saxce extends previous results of Bourgain and Gamburd for the unitary groups SU(d).

This talk is part of the Isaac Newton Institute Seminar Series series.

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